It's worth pointing out that particle-based fluid simulators are not physically accurate. They compute the positions of zero-volume particles in space at every frame (fluid has volume). This is convenient for performance purposes since you can evaluate each particle position mostly in parallel and the results look convincing enough for a movie or a game.

In contrast, mesh-based (and grid-based like in the article) simulators approximate the Navier-Stokes equations and converge to the exact solution as the mesh element sizes approach zero.

Mesh-based simulators solve a global system of equations in every frame. This system has variables equal in number to total mesh elements over the entire domain. Solving such a large system (especially in 3D) is very expensive. Furthermore, the size and shape of the mesh elements drastically affect the numerical stability of the solution, and generating good meshes is not a solved problem in all cases. For these reasons, we really only use mesh-based simulators when we need a high-degree of scientific accuracy.